SET007 Axioms: SET007+242.ax
%------------------------------------------------------------------------------
% File : SET007+242 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Filters - Part I
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : filter_0 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 128 ( 14 unt; 0 def)
% Number of atoms : 1007 ( 61 equ)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 1065 ( 186 ~; 4 |; 497 &)
% ( 23 <=>; 355 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 40 ( 38 usr; 1 prp; 0-4 aty)
% Number of functors : 32 ( 32 usr; 0 con; 1-4 aty)
% Number of variables : 349 ( 337 !; 12 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_filter_0,axiom,
? [A] :
( l3_lattices(A)
& ~ v3_struct_0(A)
& v3_lattices(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v3_filter_0(A) ) ).
fof(cc1_filter_0,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v11_lattices(A)
& v12_lattices(A) ) ) ) ).
fof(fc1_filter_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k5_filter_0(A,B,C)) ) ).
fof(fc2_filter_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A) )
=> ( ~ v3_struct_0(k8_filter_0(A,B))
& v3_lattices(k8_filter_0(A,B))
& v4_lattices(k8_filter_0(A,B))
& v5_lattices(k8_filter_0(A,B))
& v6_lattices(k8_filter_0(A,B))
& v7_lattices(k8_filter_0(A,B))
& v8_lattices(k8_filter_0(A,B))
& v9_lattices(k8_filter_0(A,B))
& v10_lattices(k8_filter_0(A,B)) ) ) ).
fof(t1_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,D,C))
& r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,D))
& r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,D,C))
& r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,C,D)) ) ) ) ) ) ) ).
fof(t2_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r3_lattices(A,k4_lattices(A,B,D),C)
& r3_lattices(A,k4_lattices(A,D,B),C) ) ) ) ) ) ) ).
fof(t3_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r3_lattices(A,B,k3_lattices(A,D,C))
& r3_lattices(A,B,k3_lattices(A,C,D)) ) ) ) ) ) ) ).
fof(t4_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& r3_lattices(A,D,E) )
=> ( r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,E))
& r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,E,C)) ) ) ) ) ) ) ) ).
fof(t5_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& r3_lattices(A,D,E) )
=> ( r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,C,E))
& r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,E,C)) ) ) ) ) ) ) ) ).
fof(t6_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& r3_lattices(A,D,C) )
=> r3_lattices(A,k3_lattices(A,B,D),C) ) ) ) ) ) ).
fof(t7_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& r3_lattices(A,B,D) )
=> r3_lattices(A,B,k4_lattices(A,C,D)) ) ) ) ) ) ).
fof(d1_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( m1_filter_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
<=> r2_hidden(k4_lattices(A,C,D),B) ) ) ) ) ) ) ).
fof(t8_filter_0,axiom,
$true ).
fof(t9_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( m1_filter_0(B,A)
<=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k4_lattices(A,C,D),B) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r3_lattices(A,C,D) )
=> r2_hidden(D,B) ) ) ) ) ) ) ) ).
fof(t10_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_filter_0(D,A)
=> ( r2_hidden(B,D)
=> ( r2_hidden(k3_lattices(A,B,C),D)
& r2_hidden(k3_lattices(A,C,B),D) ) ) ) ) ) ) ).
fof(t11_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_hidden(C,B) ) ) ) ).
fof(t12_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> r2_hidden(k6_lattices(A),B) ) ) ) ).
fof(t13_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> m1_filter_0(k6_domain_1(u1_struct_0(A),k6_lattices(A)),A) ) ) ).
fof(t14_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( m1_filter_0(k6_domain_1(u1_struct_0(A),B),A)
=> v14_lattices(A) ) ) ) ).
fof(t15_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> m1_filter_0(u1_struct_0(A),A) ) ).
fof(d2_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> k1_filter_0(A) = u1_struct_0(A) ) ).
fof(t16_filter_0,axiom,
$true ).
fof(t17_filter_0,axiom,
$true ).
fof(t18_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(B,k2_filter_0(A,C))
<=> r3_lattices(A,C,B) ) ) ) ) ).
fof(t19_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(B,k2_filter_0(A,B))
& r2_hidden(k3_lattices(A,B,C),k2_filter_0(A,B))
& r2_hidden(k3_lattices(A,C,B),k2_filter_0(A,B)) ) ) ) ) ).
fof(t20_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> k1_filter_0(A) = k2_filter_0(A,k5_lattices(A)) ) ) ).
fof(d4_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( v1_filter_0(B,A)
<=> ( B != u1_struct_0(A)
& ! [C] :
( m1_filter_0(C,A)
=> ( r1_tarski(B,C)
=> ( C = u1_struct_0(A)
| B = C ) ) ) ) ) ) ) ).
fof(t21_filter_0,axiom,
$true ).
fof(t22_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v13_lattices(A)
=> ! [B] :
( m1_filter_0(B,A)
=> ~ ( B != u1_struct_0(A)
& ! [C] :
( m1_filter_0(C,A)
=> ~ ( r1_tarski(B,C)
& v1_filter_0(C,A) ) ) ) ) ) ) ).
fof(t23_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( ~ ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_lattices(A,B,C) = B )
& k2_filter_0(A,B) = u1_struct_0(A) ) ) ) ).
fof(t24_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A)
& B != k5_lattices(A)
& ! [C] :
( m1_filter_0(C,A)
=> ~ ( r2_hidden(B,C)
& v1_filter_0(C,A) ) ) ) ) ) ).
fof(d5_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_filter_0(C,A)
=> ( C = k3_filter_0(A,B)
<=> ( r1_tarski(B,C)
& ! [D] :
( m1_filter_0(D,A)
=> ( r1_tarski(B,D)
=> r1_tarski(C,D) ) ) ) ) ) ) ) ).
fof(t25_filter_0,axiom,
$true ).
fof(t26_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> k3_filter_0(A,B) = B ) ) ).
fof(t27_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_tarski(B,C)
=> r1_tarski(k3_filter_0(A,B),k3_filter_0(A,C)) ) ) ) ) ).
fof(t28_filter_0,axiom,
$true ).
fof(t29_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(B,C)
=> r1_tarski(k2_filter_0(A,B),k3_filter_0(A,C)) ) ) ) ) ).
fof(t30_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = k6_domain_1(u1_struct_0(A),B)
=> k3_filter_0(A,C) = k2_filter_0(A,B) ) ) ) ) ).
fof(t31_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A)
& r2_hidden(k5_lattices(A),B) )
=> ( k3_filter_0(A,B) = k1_filter_0(A)
& k3_filter_0(A,B) = u1_struct_0(A) ) ) ) ) ).
fof(t32_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A)
& r2_hidden(k5_lattices(A),B) )
=> ( B = k1_filter_0(A)
& B = u1_struct_0(A) ) ) ) ) ).
fof(d6_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( v2_filter_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k3_lattices(A,C,D),B)
<=> ( r2_hidden(C,B)
| r2_hidden(D,B) ) ) ) ) ) ) ) ).
fof(t33_filter_0,axiom,
$true ).
fof(t34_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,k4_lattices(A,B,k3_lattices(A,k7_lattices(A,B),C)),C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_lattices(A,k4_lattices(A,B,D),C)
=> r3_lattices(A,D,k3_lattices(A,k7_lattices(A,B),C)) ) ) ) ) ) ) ) ).
fof(d7_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( v3_filter_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r1_lattices(A,k2_lattices(A,B,D),C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_lattices(A,k2_lattices(A,B,E),C)
=> r1_lattices(A,E,D) ) ) ) ) ) ) ) ).
fof(d8_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( D = k4_filter_0(A,B,C)
<=> ( r3_lattices(A,k4_lattices(A,B,D),C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r3_lattices(A,k4_lattices(A,B,E),C)
=> r3_lattices(A,E,D) ) ) ) ) ) ) ) ) ) ).
fof(t35_filter_0,axiom,
$true ).
fof(t36_filter_0,axiom,
$true ).
fof(t37_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> v14_lattices(A) ) ).
fof(t38_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k4_filter_0(A,B,B) = k6_lattices(A) ) ) ).
fof(t39_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> v11_lattices(A) ) ).
fof(t40_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> v3_filter_0(A) ) ).
fof(t41_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_filter_0(D,A)
=> ( ( r2_hidden(B,D)
& r2_hidden(k4_filter_0(A,B,C),D) )
=> r2_hidden(C,D) ) ) ) ) ) ).
fof(t42_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_filter_0(D,A)
=> ( r2_hidden(B,D)
=> r2_hidden(k4_filter_0(A,C,B),D) ) ) ) ) ) ).
fof(t43_filter_0,axiom,
$true ).
fof(t44_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ( r2_hidden(B,D)
& r2_hidden(C,E) )
=> ( r2_hidden(k4_lattices(A,B,C),k5_filter_0(A,D,E))
& r2_hidden(k4_lattices(A,C,B),k5_filter_0(A,D,E)) ) ) ) ) ) ) ) ).
fof(t45_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B,C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r2_hidden(B,k5_filter_0(A,C,D))
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( B = k4_lattices(A,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ) ) ) ) ).
fof(t46_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k5_filter_0(A,B,C) = k5_filter_0(A,C,B) ) ) ) ).
fof(t47_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),k3_filter_0(A,B),C))
& k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,k3_filter_0(A,C))) ) ) ) ) ).
fof(t49_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( m1_filter_0(C,A)
=> ( r1_tarski(B,k5_filter_0(A,B,C))
& r1_tarski(C,k5_filter_0(A,B,C)) ) ) ) ) ).
fof(t50_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( m1_filter_0(C,A)
=> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k3_filter_0(A,k5_filter_0(A,B,C)) ) ) ) ).
fof(t51_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( m1_filter_0(C,A)
=> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k6_filter_0(A,B,C) ) ) ) ).
fof(t52_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( m1_filter_0(C,A)
=> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k7_filter_0(A,B,C) ) ) ) ).
fof(t53_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(B,k3_filter_0(A,k4_subset_1(u1_struct_0(A),D,k6_domain_1(u1_struct_0(A),C))))
=> r2_hidden(k4_filter_0(A,C,B),k3_filter_0(A,D)) ) ) ) ) ) ).
fof(t54_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_filter_0(E,A)
=> ( ( r2_hidden(k4_filter_0(A,B,C),E)
& r2_hidden(k4_filter_0(A,C,D),E) )
=> r2_hidden(k4_filter_0(A,B,D),E) ) ) ) ) ) ) ).
fof(t55_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_filter_0(A,B,C) = k3_lattices(A,k7_lattices(A,B),C) ) ) ) ).
fof(t56_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
<=> k4_lattices(A,B,k7_lattices(A,C)) = k5_lattices(A) ) ) ) ) ).
fof(t57_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( v1_filter_0(B,A)
<=> ( B != u1_struct_0(A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
| r2_hidden(k7_lattices(A,C),B) ) ) ) ) ) ) ).
fof(t58_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ( B != k1_filter_0(A)
& v2_filter_0(B,A) )
<=> v1_filter_0(B,A) ) ) ) ).
fof(t59_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( v1_filter_0(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
<=> ~ r2_hidden(k7_lattices(A,C),B) ) ) ) ) ) ).
fof(t60_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_filter_0(D,A)
=> ~ ( v1_filter_0(D,A)
& ( ( r2_hidden(B,D)
& ~ r2_hidden(C,D) )
| ( ~ r2_hidden(B,D)
& r2_hidden(C,D) ) ) ) ) ) ) ) ) ).
fof(d10_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& l3_lattices(C) )
=> ( C = k8_filter_0(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B)
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B)
& D = k1_realset1(u2_lattices(A),B)
& E = k1_realset1(u1_lattices(A),B)
& C = g3_lattices(B,D,E) ) ) ) ) ) ) ).
fof(t61_filter_0,axiom,
$true ).
fof(t62_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_lattices(A)
& v10_lattices(A)
& l3_lattices(A) )
=> k8_filter_0(A,k1_filter_0(A)) = A ) ).
fof(t63_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( u1_struct_0(k8_filter_0(A,B)) = B
& u2_lattices(k8_filter_0(A,B)) = k1_realset1(u2_lattices(A),B)
& u1_lattices(k8_filter_0(A,B)) = k1_realset1(u1_lattices(A),B) ) ) ) ).
fof(t64_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_filter_0(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k8_filter_0(A,D)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k8_filter_0(A,D)))
=> ( ( B = E
& C = F )
=> ( k3_lattices(A,B,C) = k3_lattices(k8_filter_0(A,D),E,F)
& k4_lattices(A,B,C) = k4_lattices(k8_filter_0(A,D),E,F) ) ) ) ) ) ) ) ) ).
fof(t65_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_filter_0(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k8_filter_0(A,D)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k8_filter_0(A,D)))
=> ( ( B = E
& C = F )
=> ( r3_lattices(A,B,C)
<=> r3_lattices(k8_filter_0(A,D),E,F) ) ) ) ) ) ) ) ) ).
fof(t66_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( v14_lattices(A)
=> v14_lattices(k8_filter_0(A,B)) ) ) ) ).
fof(t67_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( v12_lattices(A)
=> v12_lattices(k8_filter_0(A,B)) ) ) ) ).
fof(t68_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( v11_lattices(A)
=> v11_lattices(k8_filter_0(A,B)) ) ) ) ).
fof(t69_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> v3_filter_0(k8_filter_0(A,B)) ) ) ) ).
fof(t70_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v13_lattices(k8_filter_0(A,k2_filter_0(A,B))) ) ) ).
fof(t71_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_lattices(k8_filter_0(A,k2_filter_0(A,B))) = B ) ) ).
fof(t72_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v14_lattices(A)
=> k6_lattices(k8_filter_0(A,k2_filter_0(A,B))) = k6_lattices(A) ) ) ) ).
fof(t73_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> v15_lattices(k8_filter_0(A,k2_filter_0(A,B))) ) ) ) ).
fof(t74_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& l3_lattices(A)
& ~ v3_struct_0(A)
& v10_lattices(A)
& v12_lattices(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k8_filter_0(A,k2_filter_0(A,B)))
& v10_lattices(k8_filter_0(A,k2_filter_0(A,B)))
& v15_lattices(k8_filter_0(A,k2_filter_0(A,B)))
& v16_lattices(k8_filter_0(A,k2_filter_0(A,B)))
& l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) ) ) ) ) ).
fof(t75_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k8_filter_0(A,k2_filter_0(A,B)))
& v10_lattices(k8_filter_0(A,k2_filter_0(A,B)))
& v17_lattices(k8_filter_0(A,k2_filter_0(A,B)))
& l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) ) ) ) ) ).
fof(d11_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_filter_0(A,B,C) = k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,C,B)) ) ) ) ).
fof(t76_filter_0,axiom,
$true ).
fof(t77_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_filter_0(A,B,C) = k9_filter_0(A,C,B) ) ) ) ).
fof(t78_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_filter_0(E,A)
=> ( ( r2_hidden(k9_filter_0(A,B,C),E)
& r2_hidden(k9_filter_0(A,C,D),E) )
=> r2_hidden(k9_filter_0(A,B,D),E) ) ) ) ) ) ) ).
fof(d12_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( v1_relat_1(C)
=> ( C = k10_filter_0(A,B)
<=> ( r1_tarski(k3_relat_1(C),u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E),C)
<=> r2_hidden(k9_filter_0(A,D,E),B) ) ) ) ) ) ) ) ) ).
fof(t79_filter_0,axiom,
$true ).
fof(t80_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(t81_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> r1_relat_2(k10_filter_0(A,B),u1_struct_0(A)) ) ) ) ).
fof(t82_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> r3_relat_2(k10_filter_0(A,B),u1_struct_0(A)) ) ) ).
fof(t83_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> r8_relat_2(k10_filter_0(A,B),u1_struct_0(A)) ) ) ) ).
fof(t84_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> ( v3_relat_2(k10_filter_0(A,B))
& v8_relat_2(k10_filter_0(A,B))
& v1_partfun1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ).
fof(t85_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A) )
=> k3_relat_1(k10_filter_0(A,B)) = u1_struct_0(A) ) ) ) ).
fof(d13_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_filter_0(A,B,C,D)
<=> r2_hidden(k9_filter_0(A,C,D),B) ) ) ) ) ) ).
fof(t86_filter_0,axiom,
$true ).
fof(t87_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_filter_0(D,A)
=> ( r1_filter_0(A,D,B,C)
<=> r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k10_filter_0(A,D)) ) ) ) ) ) ).
fof(t88_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v3_filter_0(C)
& l3_lattices(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_filter_0(E,C)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r1_filter_0(C,E,D,D)
& r1_filter_0(A,B,F,F) ) ) ) ) ) ) ) ).
fof(t89_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_filter_0(D,A)
=> ( r1_filter_0(A,D,B,C)
=> r1_filter_0(A,D,C,B) ) ) ) ) ) ).
fof(t90_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v10_lattices(C)
& v3_filter_0(C)
& l3_lattices(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_filter_0(G,C)
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( ( ( r1_filter_0(C,G,D,E)
& r1_filter_0(C,G,E,F) )
=> r1_filter_0(C,G,D,F) )
& ( ( r1_filter_0(A,B,H,I)
& r1_filter_0(A,B,I,J) )
=> r1_filter_0(A,B,H,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m1_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(existence_m1_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ? [B] : m1_filter_0(B,A) ) ).
fof(dt_k1_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> m1_filter_0(k1_filter_0(A),A) ) ).
fof(dt_k2_filter_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_filter_0(k2_filter_0(A,B),A) ) ).
fof(dt_k3_filter_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_filter_0(k3_filter_0(A,B),A) ) ).
fof(dt_k4_filter_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k4_filter_0(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k5_filter_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k5_filter_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k6_filter_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A)
& m1_filter_0(C,A) )
=> m1_filter_0(k6_filter_0(A,B,C),A) ) ).
fof(redefinition_k6_filter_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A)
& m1_filter_0(C,A) )
=> k6_filter_0(A,B,C) = k5_filter_0(A,B,C) ) ).
fof(dt_k7_filter_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A)
& m1_filter_0(C,A) )
=> m1_filter_0(k7_filter_0(A,B,C),A) ) ).
fof(redefinition_k7_filter_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A)
& m1_filter_0(C,A) )
=> k7_filter_0(A,B,C) = k5_filter_0(A,B,C) ) ).
fof(dt_k8_filter_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A) )
=> ( ~ v3_struct_0(k8_filter_0(A,B))
& v10_lattices(k8_filter_0(A,B))
& l3_lattices(k8_filter_0(A,B)) ) ) ).
fof(dt_k9_filter_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k9_filter_0(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k10_filter_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A) )
=> v1_relat_1(k10_filter_0(A,B)) ) ).
fof(dt_k11_filter_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A)
& m1_filter_0(B,A) )
=> ( v3_relat_2(k11_filter_0(A,B))
& v8_relat_2(k11_filter_0(A,B))
& v1_partfun1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(redefinition_k11_filter_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v3_filter_0(A)
& l3_lattices(A)
& m1_filter_0(B,A) )
=> k11_filter_0(A,B) = k10_filter_0(A,B) ) ).
fof(dt_k12_filter_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A) )
=> ( v3_relat_2(k12_filter_0(A,B))
& v8_relat_2(k12_filter_0(A,B))
& v1_partfun1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(redefinition_k12_filter_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A) )
=> k12_filter_0(A,B) = k10_filter_0(A,B) ) ).
fof(d3_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_filter_0(A,B) = a_2_0_filter_0(A,B) ) ) ).
fof(d9_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> k5_filter_0(A,B,C) = a_3_0_filter_0(A,B,C) ) ) ) ).
fof(t48_filter_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ! [C] :
( m1_filter_0(C,A)
=> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = a_3_1_filter_0(A,B,C) ) ) ) ).
fof(fraenkel_a_2_0_filter_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_filter_0(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r3_lattices(B,C,D) ) ) ) ).
fof(fraenkel_a_3_0_filter_0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_0_filter_0(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& A = k4_lattices(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_3_1_filter_0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B)
& m1_filter_0(C,B)
& m1_filter_0(D,B) )
=> ( r2_hidden(A,a_3_1_filter_0(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& ? [G] :
( m1_subset_1(G,u1_struct_0(B))
& r3_lattices(B,k4_lattices(B,F,G),E)
& r2_hidden(F,C)
& r2_hidden(G,D) ) ) ) ) ) ).
%------------------------------------------------------------------------------